The present invention concerns a method and a device operating by interpolation in a discrete spectrum to determine particular characteristics of a signal, such as the frequency, the amplitude or the phase, and applications of said method.
It is known that various characteristics can be determined from a processed temporal signal, in particular according to the intended applications and uses.
One of the characteristics most often used and extracted from a processed temporal signal is its frequency. This is the case in particular:
when the frequency corresponds to a physical magnitude to be evaluated, for example the beat frequency of a radioaltimeter which is proportional to the altitude to be measured or the beat frequency of Doppler effect radar which is proportional to the projection of the speed of the mobile onto the axis of the beam, or
when the signal is a modulated carrier and the frequency of the carrier is needed to demodulate the signal (for example in radiocommunication or xe2x80x9cGPSxe2x80x9d receivers).
Determining the frequency of a signal, which seems easy in theory, for example by using a frequency meter counting cycles, is often subject to major difficulties in practice, however, in particular because of interference to which the signal is subject. It is known that a temporal signal of the above kind is often subject to very high levels of interference, in particular caused by:
noise, in particular the intrinsic noise of a transmit and receive system used, and/or
spurious signals, for example echoes from objects other than the ground in the case of a radioaltimeter, and/or
other signals, for example sidebands of a modulated carrier.
To solve these interference problems at least in part, the signal is often subjected to discrete Fourier transformation to obtain a discrete spectrum which simplifies determination of the frequency.
In many systems the signal is sampled and digitized, and this often applies at the beat signal stage, and all subsequent processing is performed in the digital domain, usually by means of dedicated processors.
The following devices that can use digital processing may be cited as examples: radioaltimeters, xe2x80x9cGPSxe2x80x9d receivers, radiocommunication receivers, in particular those using satellites, and Doppler effect radar (onboard velocity measurement or surveillance radar).
In the manner known in itself, measuring the frequency of the signal then consists in identifying in the spectrum obtained by the Fourier transformation of the signal the rank of the component with the greatest amplitude. This rank corresponds directly to a frequency.
However, because of the discrete nature of the spectrum, the measurement resolution is limited to the value of the frequency increment used.
Moreover, the amplitude measured in the spectrum is falsified if the frequency of the signal is not an integer multiple of the frequency increment.
In the manner known in itself, to improve resolution:
either the sampling frequency is reduced, which reduces the analysis range in the same proportions, however,
or the size of the Fourier transform is increased, which significantly increases the computation load, however.
The present invention concerns a solution based on a particular frequency domain interpolation of the discrete spectrum which has the particular object of improving the resolution of the estimation of the frequency of the signal without reducing the sampling frequency and/or increasing the size of the Fourier transform.
There are various prior art solutions to the problem of frequency domain interpolation processing of a discrete spectrum.
They include:
interpolation on three adjacent samples around a local maximum, with a quadratic interpolation function (document U.S. Pat. No. 5,598,441) or a Gaussian interpolation function (document EP-0 399 704), or
interpolation on the two samples adjacent a local maximum, with the interpolation function being an approximation of the Fourier transform of the Hamming window (document U.S. Pat. No. 5,576,978).
However, all the interpolation functions used in these prior art methods are determined empirically and therefore represent approximations, a source of errors. Consequently, these prior art solutions are not sufficiently accurate.
The object of the present invention is to remedy these drawbacks. It concerns a method of determining, characteristics of a signal, in particular its frequency, accurately, at low cost, with high resolution, and without increasing the computation load, which method is suitable for any type of signal and regardless of the characteristic to be determined.
To this end the method in accordance with the invention of determining l characteristics Pq of a signal s(t,Pq) where q is an integer between 1 and l, l is an integer greater than or equal to 1 and t is time, the signal s(t,Pq) being transformed into a discrete spectrum by Fourier transformation, is remarkable in that:
a) m elements z(fi) of said discrete spectrum are selected where i is an integer between 1 and m and m is an integer greater than or equal to 2,
b) a system of m equations is determined respectively relating to said m elements z(fi) selected and defined on the basis of the relations:
z(fi)=Fi[w(t).s(t,Pq)].h(f),
i varying from 1 through m, in which:
Fi is a discrete Fourier transform,
w(t) is a temporal weighting function, and
h(f) is a frequency transfer function of an anti-aliasing filter, and
c) the l characteristics Pq are deduced from said system of m equations in l unknowns.
Accordingly, as the present invention is based, in so far as the calculations performed are concerned, not on an empirical approximation like the aforementioned prior art solutions, but on a rigorous mathematical solution, it increases the accuracy of the measurement of the characteristics Pq, which additionally necessitates only a few multiplications and additions, compared to the several hundred multiplications needed by a large Fourier transform, which therefore reduces the processing time.
The invention also reduces the calculation load and thus enables the use of a less powerful and less costly processor than the prior art solutions.
Although it improves the accuracy of the measurements of many characteristics, such as the amplitude or the phase of a signal, for example, the present invention is particularly suitable for the measurement of frequency, of which it improves the resolution and the accuracy.
Moreover, the method of the invention can easily be adapted to suit any type of processed signal, regardless of the characteristics to be examined, since in particular it is possible to use any type of temporal weighting function, for example a rectangular, triangular, Hamming or Blackman-Harris function.
Moreover, to improve the resolution, in accordance with the invention, a local maximum and that of the two elements adjacent to this local maximum whose modulus is greater are preferably selected to obtain the best signal/noise ratio.
The aforementioned processing can advantageously be simplified by carrying out the following operations:
when the numbers m and l are equal, the characteristics Pq that do not comprise the phase of the signal s(t,Pq) are determined from exact solutions of said system of m scalar equations based on the equality of the moduli,
when the number m is greater than the number l the characteristics Pq that do not comprise the phase of the signal s(t,Pq) are determined by minimizing in said system of equations an error between the values of the various elements z(fi) respectively obtained from the discrete spectrum and calculated from the corresponding equations,
when the number l is equal to the number 2m the characteristics Pq comprising the phase of the signal s(t,Pq) are determined from exact solutions of the 2m scalar equations obtained from the m complex equations z(fi), and
when the number l is greater than the number 2m the characteristics Pq comprising the phase of the signal s(t,Pq) are determined by minimizing in said system of equations an error between the values of the various elements z(fi) respectively obtained from the discrete spectrum and calculated from the corresponding equations.
Moreover, when the signal is periodic, in a particularly advantageous first embodiment of the invention, the Fourier transform of said period signal s(t,Pq) is treated as a Dirac pulse localized at a frequency fo, of amplitude A and of phase xcfx86 and the parameters Pq are determined from the m equations:
z(fi)=Aejxcfx86w(fixe2x88x92fo)
w(f) being the Fourier transform of the temporal weighting function w(t).
In this case, to determine only the frequency fo and the amplitude A of the signal s(t,Pq), it is preferable to select two elements z(fi) and z(fj) and to solve the following system of equations:
|z(fi)|=A|w(fixe2x88x92fo)|
|z(fj)|=A|w(fjxe2x88x92fo)|
Moreover, to simplify the calculations, it is advantageous to determine the relation between the function r=z(fi)/z(fj) and the frequency numerically and to determine the frequency and the amplitude of the signal from this function.
Furthermore, in a second embodiment, for a periodic signal s(t,Pq) it is advantageous to treat the Fourier transform of said periodic signal s(t,Pq) as a pair of Dirac pulses localized at respective frequencies (+fo) and (xe2x88x92fo), of common amplitude A and of phase xcfx86 and to determine the parameters Pq from the m equations:
z(fi)=Aejxcfx86(w(fixe2x88x92fo)+w(fi+fo)),
w(f) being the Fourier transform of the weighting coefficient w(t).
In this case, to determine only the frequency fo and the amplitude A of the signal s(t,Pq), it is preferable to select two elements z(fi) and z(fj) and to solve the following system of equations:
|z(fi)|=A|w(fixe2x88x92fo)+w(fi+fo)|
|z(fj)|=A|w(fjxe2x88x92fo)+w(fj+fo)|
The present invention also concerns a device for implementing the aforementioned method.
In accordance with the invention, said device is remarkable in that it includes:
means for performing temporal weighting consisting in multiplying the signal s(t,Pq) by a temporal weighting function w(t),
means for performing a Fourier transformation of the result of said temporal weighting, and
means for deducing therefrom the l characteristics Pq, as well as:
means for low-pass filtering the signal s(t,Pq),
means for sampling said signal, and
means for finding the element from the spectrum having the highest modulus.
The present invention can be applied to a very large number of systems and in particular to any frequency measurement and determination system based on digital spectral analysis of a signal.
More particularly, the method of the invention can be used in a radioaltimetric measurement method to determine the frequency used to calculate the altitude, requiring no additional component.
Moreover, said method can be used in a laboratory spectrum analyzer including:
a pre-amplifier,
a sampling device,
an analogue/digital converter,
a processor, and
a graphic device for displaying the spectrum.
In this case, in accordance with the invention, a function is added to said processor to determine by the aforementioned method particular characteristics of the signal, such as the effective amplitude and the effective frequency of a local maximum in the spectrum. Also, these characteristics can be numerically displayed by the display device, for example.
Accordingly, using the invention on an analyzer of the above kind does not require any additional hardware compared to a standard analyzer architecture and is therefore of low cost.